MH 10th Question Paper June 2026 Maths Part 2 (Geometry)

FOR MAHARASHTRA BOARD (MSBSHSE) CLASS 10 EXAM PREPARATION

Maharashtra Board
(MSBSHSE) Class 10
2026
June Session Question
Paper · Maths Part 2
(Geometry)
EXAM YEAR

Maharashtra Board (MSBSHSE) Class 10 2026
TYPE SUBJECT

June Session Question Paper Maths Part 2 (Geometry)

Notes · Sample Papers · Previous Year Papers · Mock Tests

. c s e
m a
se l

ag
Page No. 1/6 Subject code N 397 Seat No.

DATE : 23/06/2026 SUBJECT : MATHEMATICS (71) GEOMETRY—PART II (E)

TIME : 11.00 SYLLABUS : (REVISED COURSE)
DURATION : 2 Hours TOTAL PAGES : 6 TOTAL MARKS : 40
m
.co
Note :— (i) All questions are compulsory.

o m
c em
(ii) Use of a calculator is not allowed.

m . s
(iii) The numbers
e
to the right of questions indicate full marks.
(iv) sIn case of MCQs [Q. No. 1(A)] only the first attempt will be evaluated
g l a
la will be given credit. a and
g
a(v) Draw proper figures wherever necessary.
(vi) The marks of construction should be clear. Do not erase them.
(vii) Diagram is essential for writing the proof of the theorem.

1. (A) Choose the correct alternative from the given : 4
(i) Out of the following which is a Pythagorean triplet ?
(a) (1, 5, 10) (b) (5, 12, 13)
(c) (2, 3, 4)
. c om(d) (5, 5, 2)
(ii)
m
What is the measure of semicircular arc of a circle ?
e
(a) 360º
l as (b) 90º

(iii)
(c) 180º
a g
What is the equation of Y-axis ?
(d) 60º

(a) x = 0 (b) x = a
(c) y = 0 (d) y = b
(iv) Radius of a sector of a circle is 35 cm and length of its arc is 22 cm. What
is the area of the sector ?
(a) 285 cm2 (b) 185 cm2
(c) 385 cm2 (d) 85 cm2
m
.co
(B) Solve the following sub-questions : 4

. c om (i) Find the diagonal of square whose side is 5 cm.
e m
e m (ii)
a
In the following figure, seg AE  seg BC , seg DF  line BC , AE = 4,
l s
las A ( ABC)
ag
ag DF = 6, then find A ( DBC) .

D
A

B E C F

End of Page 1 (PTO)

m .
.co e m
em
For more Question Papers, Sample Papers, Notes & Syllabus visit
as
Page 1 of 6

Page No. 2/6 Subject code N 397
(iii) In the following figure, ray PQ touches the circle at point Q, PQ = 12,
PR = 9. Find PS.
S
R
P

Q
(iv) Angle made by the line with the positive direction of X-axis is 30º. Find slope
of the line.

2. (A) Complete the following activities and rewrite it (any two) : 4
(i) In the following figure, chord EN and chord FS intersect each other at point
M in the exterior of the circle.
If m (arc NS) = 125º, m (arc EF) = 37°, then complete the following activity
to find NMS.
N
E
M
F
S
Activity : Chord EN and chord FS intersect each other at point M in the
exterior of the circle.
1 
m NMS =  m(arc EF)
2 
1 
=  37
2
1
= 
2
 m NMS =
20
(ii) If sin   , then complete the following activity to find cos  .
29
Activity : sin 2   cos2   1

   cos2   1
2

400
 cos2   1
841
 cos2   1 –
cos2  
Taking square roots of both sides
 cos  

End of Page 2

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 6

. c s e
m a
se l

ag
Page No. 3/6 Subject code N 397 Seat No.

(iii) In the following figure, point O is the centre of the circle, AOB = 100º.
Complete the following activity with the help of given figure.
Y

m
m .co
.co
O

e m
em
100º
l as
s
A B

l a ag
ag Activity :
X

Type of arc Name of the arc Measure of the arc
Minor arc
Major arc

(B) Solve the following sub-questions (any four) : 8

(i)
m
In the following figure, in  PQR, seg RS bisects R. If PR = 15, QR = 20,
PS = 12, then find QS.
m .co
s e
R

g la
a
P S Q
(ii) Find the length of diagonal of a rectangle whose length is 35 cm and breadth
is 12 cm.
(iii) In the following figure, point G, D, E, F are concyclic points of a circle with
m
.co
centre C. ECF = 70º, m (arc DGF) = 200º. Find m (arc DE).
m
m .co s e m
s e D
C
G

g l a
g la a
a E
F

(iv) Find the distance between the points P (–1, 1) and Q (5, –7).

(v) A person is standing at a distance of 80 m from a Church looking at its top.
The angle of elevation is of 45º. Find the height of the Church.

End of Page 3 (PTO)

m .
.co e m
em
For more Question Papers, Sample Papers, Notes & Syllabus visit
as
Page 3 of 6

Page No. 4/6 Subject code N 397
3. (A) Complete the following activities and rewrite it (any one) : 3
(i) In the following figure, in  ABC ray BD bisects ABC, A – D – C,
AB AE
seg ED  side BC , A – E – B, then to prove that  , complete the
BC EB
following activity.
A

D
E

B C
Activity : In  ABC, ray BD bisects B.
AB
 = .............. (I) (Angle bisector theorem)
BC

In  ABC, seg ED  side BC .
AE
 = .............. (II)
EB DC
AB
 = .............. from (I) and (II)
EB
(ii) If P is the midpoint of segment joining the points A (–4, 2) and B (6, 2), then
complete the following activity to find the co-ordinates of point P.
Activity : In the given example,
suppose

A P B
(–4, 2) ( x, y ) (6, 2)
(x1, y1) = (–4, 2), (x2, y2) = (6, 2) and
Let co-ordinates of P are (x, y).
According to midpoint formula,
x1  x2  2
x = = =
2 2 2
x =
y1  y2  4
y = = =
2 2 2
y =
 Co-ordinates of midpoint are (1, 2).

End of Page 4

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 6

. c s e
m a
se l

ag
Page No. 5/6 Subject code N 397 Seat No.

(B) Solve the following sub-questions (any two) : 6

(i) In  PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13,
find QR.
m
.co
(ii) Prove that, opposite angles of a cyclic quadrilateral are supplementary.
m
(iii)
m .co
Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw
s e m
s e tangents to the circle at point P and Q. Write your observation aboutglathe
g la tangents. a
a (iv) In the following figure if A (P – ABC) = 154 cm , radius of the circle is 14
2

cm, find : (a) m APC, (b) l(arc ABC).

P
C

Bm
. c o
m
A

s e two) :
4. Solve the following sub-questions
l a (any 8

(i) ag l intersects side AB and side AC of  ABC in points
In the following figure, line
A ( APQ) AP  AQ
P and Q respectively. Show that A ( ABC)  AB  AC .

A

Q l
P

m
m .co
m .co B
s em C

e Draw a circle having radius 3 cm. Draw chord XY = 5 cm.la
las (ii)
a g Draw tangents to a circle

ag at point X and Y without using centre.

(iii) Find the number of coins of 2.2 cm diameter and 0.2 cm thick, can be made
by melting a metallic right circular cylinder of height 0.2 m and diameter
8.8 cm.

End of Page 5 (PTO)

m .
.co e m
em
For more Question Papers, Sample Papers, Notes & Syllabus visit
as
Page 5 of 6

Page No. 6/6 Subject code N 397
5. Solve the following sub-questions (any one) : 3

(i) AB is a chord of a circle with centre O. AC is a diameter of a circle. Line AT is
a tangent at A. Write the answers of the following questions :

(a) Draw the figure using the given information.

(b) Find the measure of CAT.

(c) Find the measure of ABC.

(ii)  is acute angle. If 3sin   4 cos   0 , then find the values of tan  and sec  .

End of Page 6

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 6